The primary draw back to a simple hair rig that rests on the bottom of the lake or river is the bait sitting down in the mud, silt, vegetation, etc. and the fish doesn't see it as an easy opportunity.
I still manage to catch my share of carp with the simple rig, but I am sure I can improve my catch rate by branching out into some more flexible rigs.
I am committed to using the blow back rig as my "go to" rig next year. This winter will be spent mastering this rig and tying up as many as possible to prepare for next carp fishing season, which in this part of country really doesn't get started in earnest until mid-April.
Here is a video that provides step-by-step details for the blow back rig that my friend Adam uses. This rig caught a 53 pound common carp this year on the Susquehanna River in Pennsylvania.